Frédéric Saubion

Danièle Gardy, Frédéric Lardeux, Frédéric Saubion

Initially introduced by Peter Hammer, Logical Analysis of Data is a methodology that aims at computing a logical justification for dividing a group of data in two groups of observations, usually called the positive and negative groups. Consider this partition into positive and negative groups as the description of a partially defined Boolean function; the data is then processed to identify a subset of attributes, whose values may be used to characterize the observations of the positive groups against those of the negative group. LAD constitutes an interesting rule-based learning alternative to classic statistical learning techniques and has many practical applications. Nevertheless, the computation of group characterization may be costly, depending on the properties of the data instances. A major aim of our work is to provide effective tools for speeding up the computations, by computing some \emph{a priori} probability that a given set of attributes does characterize the positive and negative groups. To this effect, we propose several models for representing the data set of observations, according to the information we have on it. These models, and the probabilities they allow us to compute, are also helpful for quickly assessing some properties of the real data at hand; furthermore they may help us to better analyze and understand the computational difficulties encountered by solving methods. Once our models have been established, the mathematical tools for computing probabilities come from Analytic Combinatorics. They allow us to express the desired probabilities as ratios of generating functions coefficients, which then provide a quick computation of their numerical values. A further, long-range goal of this paper is to show that the methods of Analytic Combinatorics can help in analyzing the performance of various algorithms in LAD and related fields.

Thomas Landais, Olivier Goudet, Adrien Goëffon et al.

Combinatorial black-box optimization in high-dimensional settings demands a careful trade-off between exploiting promising regions of the search space and preserving sufficient exploration to identify multiple optima. Although Estimation-of-Distribution Algorithms (EDAs) provide a powerful model-based framework, they often concentrate on a single region of interest, which may result in premature convergence when facing complex or multimodal objective landscapes. In this work, we incorporate the Stein operator to introduce a repulsive mechanism among particles in the parameter space, thereby encouraging the population to disperse and jointly explore several modes of the fitness landscape. Empirical evaluations across diverse benchmark problems show that the proposed method achieves performance competitive with, and in several cases superior to, leading state-of-the-art approaches, particularly on large-scale instances. These findings highlight the potential of Stein variational gradient descent as a promising direction for addressing large, computationally expensive, discrete black-box optimization problems.

Rita-Nathalia Assaf, Tom Davot, Frédéric Lardeux et al.

In this paper, we introduce position graphs, a graph-based reasoning framework based on the formalization of position spaces. This framework utilizes two strict partial orders, representing horizontal and vertical alignment and precedence, to model the relative positions of discrete tokens. Unlike general qualitative spatial calculi, position graphs are constrained by a chain condition and compatibility requirements that focus on rows and columns. We provide a comprehensive theoretical analysis of this representation, beginning with a characterization of graph consistency. Conditions to ensure the consistency of position graphs are established. Furthermore, we investigate the computational complexity of structural pattern discovery, modeled as the induced subgraph isomorphism problem. We demonstrate that this problem remains NP-complete even within the restricted class of position graphs. While initially motivated by document processing, this work focuses on the underlying mathematical properties and algebraic consistency of position-based constraints, providing a formal logical layer that is independent of specific data extraction techniques.

Axel Guérin, Pierre Chauvet, Frédéric Saubion

Self-organising maps are a powerful tool for cluster analysis in a wide range of data contexts. From the pioneer work of Kohonen, many variants and improvements have been proposed. This review focuses on the last decade, in order to provide an overview of the main evolution of the seminal SOM algorithm as well as of the methodological developments that have been achieved in order to better fit to various application contexts and users' requirements. We also highlight a specific and important application field that is related to commercial use of SOM, which involves specific data management.

Olivier Goudet, Quentin Suire, Adrien Goëffon et al.

We introduce an order-invariant reinforcement learning framework for black-box combinatorial optimization. Classical estimation-of-distribution algorithms (EDAs) often rely on learning explicit variable dependency graphs, which can be costly and fail to capture complex interactions efficiently. In contrast, we parameterize a multivariate autoregressive generative model trained without a fixed variable ordering. By sampling random generation orders during training - a form of information-preserving dropout - the model is encouraged to be invariant to variable order, promoting search-space diversity and shaping the model to focus on the most relevant variable dependencies, improving sample efficiency. We adapt Generalized Reinforcement Policy Optimization (GRPO) to this setting, providing stable policy-gradient updates from scale-invariant advantages. Across a wide range of benchmark algorithms and problem instances of varying sizes, our method frequently achieves the best performance and consistently avoids catastrophic failures.

Mohamed Salim Amri Sakhri, Adrien Goëffon, Olivier Goudet et al.

This paper explores a novel approach aimed at overcoming existing challenges in the realm of local search algorithms. Our aim is to improve the decision process that takes place within a local search algorithm so as to make the best possible transitions in the neighborhood at each iteration. To improve this process, we propose to use a neural network that has the same input information as conventional local search algorithms. In this paper, which is an extension of the work presented at EvoCOP2024, we investigate different ways of representing this information so as to make the algorithm as efficient as possible but also robust to monotonic transformations of the problem objective function. To assess the efficiency of this approach, we develop an experimental setup centered around NK landscape problems, offering the flexibility to adjust problem size and ruggedness. This approach offers a promising avenue for the emergence of new local search algorithms and the improvement of their problem-solving capabilities for black-box problems. The last version of this article is published in the journal SN Computer Science (Springer).

Giacomo di Tollo, Frédéric Lardeux, Jorge Maturana et al.

The balance of exploration versus exploitation (EvE) is a key issue on evolutionary computation. In this paper we will investigate how an adaptive controller aimed to perform Operator Selection can be used to dynamically manage the EvE balance required by the search, showing that the search strategies determined by this control paradigm lead to an improvement of solution quality found by the evolutionary algorithm.

Adrien Goëffon, Frédéric Lardeux, Frédéric Saubion

In this paper, we propose a model for simulating search operators whose behaviour often changes continuously during the search. In these scenarios, the performance of the operators decreases when they are applied. This is motivated by the fact that operators for optimization problems are often roughly classified into exploitation operators and exploration operators. Our simulation model is used to compare the different performances of operator selection policies and clearly identify their ability to adapt to such specific operators behaviours. The experimental study provides interesting results on the respective behaviours of operator selection policies when faced to such non stationary search scenarios.